Solve for $x$ and $y$ using elimination. ${x+4y = 18}$ ${2x+3y = 21}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-2$ ${-2x-8y = -36}$ $2x+3y = 21$ Add the top and bottom equations together. $-5y = -15$ $\dfrac{-5y}{{-5}} = \dfrac{-15}{{-5}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {x+4y = 18}\thinspace$ to find $x$ ${x + 4}{(3)}{= 18}$ $x+12 = 18$ $x+12{-12} = 18{-12}$ ${x = 6}$ You can also plug ${y = 3}$ into $\thinspace {2x+3y = 21}\thinspace$ and get the same answer for $x$ : ${2x + 3}{(3)}{= 21}$ ${x = 6}$